The sound velocity of wüstite at high pressures: implications for low-velocity anomalies at the base of the lower mantle

The longitudinal sound velocity (VP) and the density (ρ) of wüstite, FeO, were measured at pressures of up to 112.3 GPa and temperatures of up to 1700 K using both inelastic X-ray scattering and X-ray diffraction combined with a laser-heated diamond-anvil cell. The linear relationship between VP and ρ, Birch’s law, for wüstite can be expressed as VP = 1.55 (1) × ρ [g/cm3] − 2.03 (8) [km/s] at 300 K and VP = 1.61 (1) × ρ [kg/m3] − 2.82 (10) [km/s] at 1700 K. The sound velocity of wüstite is significantly lower than that of bridgmanite and ferropericlase under lower mantle conditions. In other words, the existence of wüstite in the lower mantle can efficiently decrease the seismic velocity. Considering its slow velocity and several mechanisms for the formation of FeO-rich regions at the core–mantle boundary, we confirm earlier suggestions indicating that wüstite enrichment at the bottom of the Earth’s mantle may contribute to the formation of denser ultra-low velocity zones.


Introduction
Wüstite, FeO, is one of the most important oxides in the interior of the Earth because it is an endmember of ferropericlase, (Mg,Fe)O, which is the second most dominant phase in the Earth's lower mantle. Wüstite has a B1 (NaCl-type) structure under ambient conditions. Under increasing pressure, it distorts into rB1 (a rhombohedral distorted-B1 phase) at approximately 16 GPa (e.g., Yagi et al. 1985), and a phase transition from rB1 to a B8 (NiAs-type) structure has been found at 96 GPa and 800 K (e.g., Fei and Mao 1994). The phase transformation from B8 into a B2 (CsCl-type) structure has been observed, and the triple point for the B1, B8, and B2 phases has been reported to be at 240 GPa and 3800 K (Ozawa et al. 2011b). In B8-FeO, an occurrence of iron spin crossover, inversenormal structural transition, and insulator-metal transition has been reported near 120 GPa (Ozawa et al. 2011a). In addition, the metallization of B1-FeO has been found near 70 GPa and 1900 K without any structural phase transition (Ohta et al. 2012).
Seismological studies reveal the density and the sound velocity within the interior of the Earth and allow us to discuss its heterogeneous structure. For example, ultralow velocity zones (ULVZs) at the core-mantle boundary (CMB) have been observed (e.g., Idehara et al. 2007;Hutko et al. 2009;Rost et al. 2010; Thorne and Garnero 2004). The thickness of ULVZs is 5 − 20 km, and the V P and V S values in these zones decrease by~5% − 20% and 10% − 30%, respectively. Even though ULVZs are locally distributed, (e.g., under the Philippine-Kalimantan and East Australia regions (Idehara et al. 2007); the central and north Pacific (Hutko et al. 2009); and east of Australia (Rost et al. 2010)), some ULVZs are likely attributable to wüstite enrichment in the mantle (e.g., Knittle and Jeanloz 1991;Dobson and Brodholt 2005;Labrosse et al. 2007). One important phenomenon is the chemical reaction between the silicates in the lower mantle and the liquid outer core; indeed, the formation of FeO has been experimentally demonstrated using a laser-heated diamondanvil cell (LHDAC) (e.g., Knittle and Jeanloz 1991). Banded-iron formations (BIFs) in subducting slabs can also provide FeO to the lower mantle due to the reduction of the Fe 3 O 4 components in BIFs (Dobson and Brodholt 2005). A crystallization of a very dense iron-rich layer has also been proposed via the basal magma ocean hypothesis (Labrosse et al. 2007). In addition, the decomposition of ferropericlase, (Mg 0.05 ,Fe 0.95 )O, into FeO and (Mg 0.20 , Fe 0.80 )O has been observed in LHDAC experiments (Ohta et al. 2014). Therefore, knowledge of the elasticity of wüstite under lower mantle conditions will allow a better understanding of ULVZs.
Sound velocity measurements of ferropericlase (e.g., Jackson Lin et al. 2006) and magnesiowüstite (e.g., Wicks et al. 2010Wicks et al. , 2017 have been reported. Ferropericlase, which is iron-poor (Mg,Fe)O, undergoes a spin crossover, resulting in a volume reduction and a change in physical properties, such as the sound velocities and density (e.g., Jackson et al. 2006;Lin et al. 2006). In addition, the sound velocity of wüstite has been measured at room temperature using various methods, such as the rectangular parallelepiped resonance method (Sumino et al. 1980) and ultrasonic velocity measurements (Mizutani et al. 1972). For sound velocity measurements at high pressure, the combination of a diamond-anvil cell (DAC) and inelastic X-ray scattering (IXS) is a powerful technique (e.g., Badro et al. 2007). Even though the velocity of wüstite has been measured up to 90 GPa (Badro et al. 2007), such measurements remain limited to ambient temperatures and hightemperature data are still unavailable. Here, we conduct IXS experiments using LHDAC to obtain the sound velocity of wüstite at high pressure and high temperature to understand possible implications for the low-velocity anomalies at the CMB.

Methods/Experimental
The starting sample was a wüstite powder made from a reduction of hematite in a gas-controlled electric furnace. The chemical composition of the powder sample was confirmed to be Fe 0.92 O based on the lattice parameter determined via X-ray diffraction (McCammon and Liu 1984). A symmetric-type DAC was used to generate the examined pressures. The culet sizes of the diamond anvils were 150-300 μm, depending on the target pressure. Tungsten or rhenium was used as a gasket with a drilled hole for a sample chamber. The thickness and diameter of the sample chamber were approximately one-fourth and one-third of the culet sizes, respectively. The initial thickness of the samples was approximately 10-20 μm. The samples were loaded between two layers of NaCl or Al 2 O 3 , which were used as the pressure medium and thermal insulator. The pressure mediums were 15-25 μm thick.
IXS experiments were performed on the BL35XU beamline (Baron et al. 2000) at the SPring-8 facility in Japan. The beam size was focused to 16 μm × 16 μm using a pair of Kirkpatrick-Baez mirrors (Ishikawa et al. 2013). The Si (9 9 9) backscattering optics provided an incident photon energy of 17.79 keV with an energy resolution of 3 meV at full width at half maximum (FWHM). A 3 × 4 array of spherical analyzer crystals was set at the end of the horizontal arm to analyze the scattered X-rays with different scattering vectors. The momentum transfer, Q = 2k 0 sin(2θ/2), where k 0 is the wave number of the incident photons and 2θ is the scattering angle, was selected by rotating the spectrometer arm in the horizontal plane. The momentum resolution was set to an approximately 0.4 nm −1 full width using slits in front of the analyzers. In this study, IXS spectra were collected in the range of Q = 4.0-10.0 nm −1 at each experimental pressure. X-ray diffraction (XRD) patterns were also obtained under the same experimental conditions as IXS using a flat panel area detector installed at BL35XU. The experimental pressure was determined using the unit cell volume of wüstite determined via XRD and its equation of state (McCammon and Liu 1984;Stixrude and Lithgow-Bertelloni 2007;Fischer et al. 2011). The parameters used for the equation of state of B1-FeO are summarized in Table 1. We also checked the experimental pressure using the equation of state of NaCl (B1, Matsui et al. 2012;B2, Sakai et al. 2011) and a diamond Raman gage (Akahama and Kawamura 2004). A portable laser heating system, COMPAT , was installed on the beamline to generate high temperatures. This system enabled us to measure the IXS from the sample loaded in the DAC under high pressure and high-temperature conditions (Sakamaki et al. 2016;Sakairi et al. 2018;Takahashi et al. 2019). The average diameter of the hot spot was approximately 30 μm, which was larger than the size of the incident X-ray beam. The typical temperature

Results and discussion
The IXS spectra of wüstite were acquired in the pressure range from 4.1 GPa to 112.3 GPa and the temperature range from 300 K to 1700 K. The experimental conditions and results are summarized in Table 2. All samples under the experimental conditions were identified as having the B1 phase based on their XRD patterns. The density of wüstite was calculated using the unit cell volume obtained via XRD at the same conditions as the IXS measurements. An example of the IXS spectra and XRD pattern at 59.4 GPa and 1700 K is shown in Figs. 1 and 2, respectively. The IXS spectra are characterized by an elastic contribution centered at zero energy and inelastic contributions from the longitudinal acoustic (LA) mode of wüstite and the transverse acoustic (TA) mode from the diamond anvil. Each peak energy position of the photons was obtained by fitting a Lorentzian function to the peak. The longitudinal sound velocity (V P ) was calculated by fitting the phonon dispersion (Fig. 3) with a function, where E and Q are the energy and momentum transfer, respectively, and Q max is a free parameter. Our result at 4 GPa is compared to those of previous studies under ambient conditions in Fig. 4. Considering the pressure dependence of V P , the velocity found in this study at 4 GPa is approximately 0.1 km/s larger than that of the ambient data. The velocities are in the range of 6.4-6.7 km/s except in the study of Badro et al. (2007). Sumino et al. (1980) reported that the density and velocity of wüstite increased with the decreasing fraction of iron deficiency in the wüstite: Fe 0.92 O had ρ = 5.68 g/ cm 3 and V P = 6.54 km/s and FeO had ρ = 5.86 g/cm 3 and V P = 6.63 km/s. Our result is consistent with the trend reported by Sumino et al. (1980). The variation of ρ-V P shown in Fig. 4 may be caused by differences in the sample conditions and/or measurement techniques.
The measured velocities are plotted as a function of density in Fig. 5. For comparison, data from previous studies (Badro et al. 2007;Wicks et al. 2017) are also plotted. The V P -ρ relationship for our study shows a similar trend that of Badro et al. (2007), whereas the trend found by Wicks et al. (2017) is different with a density (pressure) dependence that is much smaller than that seen in our data. Our study and that of Badro et al. (2007) calculated V P based on the phonon dispersion obtained via the IXS measurement. Conversely, Wicks et al. (2017) conducted nuclear resonance inelastic scattering (NRIXS) experiments and acquired the Debye sound velocity using the low-energy regions of the phonon density of states. There is a possibility that the differences in the techniques used contributed to the discrepancies between the high-pressure data.
The V P -ρ data at ambient temperature in this study show a linear relationship, following Birch's law (Birch 1961), which is expressed as Assuming that the V P -ρ data at 1700 K also follow Birch's law, the linear relationship at 1700 K can be expressed as Assuming a linear temperature dependence, the isothermal V P -ρ fitting line at a temperature T [K] can be expressed as Transverse sound velocities (V S ) of wüstite were obtained such that K S is the adiabatic bulk modulus and is calculated as where α is the coefficient of thermal expansion (Seagle et al. 2008), γ is the Grüneisen parameter, and K T is the isothermal bulk modulus (Fischer et al. 2011). The thermal expansion of FeO is known to be approximately independent of temperature above 1620 K (Seagle et al. 2008). The coefficient of thermal expansion at high pressure is calculated using the following form: α = α 0 (V/ V 0 ) ξ (where α 0 = 4.22 × 10 −5 K −1 , V 0 = 84.75 3 , and ξ = 6.0; Seagle et al. 2008).
The V S -ρ relationship in this study also follows Birch's law and the linear relationships at 300 K and 1700 K are described as Applying the same isothermal fitting to V S -ρ, the following equation is obtained: According to Fig. 4, the misfit in V P at 300 K between the study of Badro et al. (2007) and the other studies is approximately 0.3-0.4 km/s. This misfit is large compared to the estimated errors. Even though there are several possibilities for this misfit, the differences between this study and that of Badro et al. (2007) can be, at least qualitatively, understood by considering distinctions in the spectrometer operations. Even though the IXS spectrometers at both SPring-8 and ESRF operate in backscattering geometry and scan energies by varying the temperature of the main monochromator, technical aspects directly influence the temporal stability of the elastic energy and the data collection. Another significant difference is in the number and relative positions used to constrain the phonon dispersion within the first Brillouin zone. We used four points in the 4-8 nm −1 range, while Badro et al. (2007) used five points in the 4-12 nm −1 range. As described in Bosak et al. (2007), the V P value is sensitive to the dispersion fitting procedure and the Q-settings can affect the derived velocity. Figure 5 shows that the V P and V S values at high pressure reported by Wicks et al. (2017) are approximately 20-30% smaller than the velocities in our study and that of Badro et al. (2007). The misfit is clearly larger than the estimated errors. For the velocity measurement, Wicks et al. (2017) conducted NRIXS, which probes the partial projected phonon density of states of materials containing Mössbauer resonant isotopes (e.g., 57 Fe). The Debye velocity can be obtained via a parabolic fit of the low-energy portions of the phonon density of states. Combining the measured Debye velocity with an equation of state (density and adiabatic bulk modulus), V P and V S can be determined. In other words, the V P and V S values are dependent on the choice of the equation of state used for the data analysis. In terms of the velocities at high pressure, Wicks et al. (2017) used an approximately 20% smaller bulk modulus than the equation of state reported by Fischer et al. (2011). This implies that Wicks et al. (2017) underestimated the V P and V S values at high pressure.
The sound velocities of wüstite and the lower mantle minerals as a function of pressure along the representative mantle geotherm (Brown and Shankland 1981) are shown in Fig. 6. The velocities of (Mg 0.94 ,Fe 0.06 )SiO 3 bridgimanite and (Mg 0.79 ,Fe 0.21 )O ferropericlase have been reported by Murakami et al. (2007). Under lower mantle conditions, the V P and V S values of wüstite are lower than those of bridgimanite and ferropericlase.
The calculated V P and V S values of wüstite along the mantle geotherm are compared to PREM and ULVZs in Fig. 7. The V P and V S values of wüstite are 19% and 27% lower than those of PREM under CMB conditions (P = 136 GPa and T = 2450 K), respectively. The velocity reduction at the ULVZs (V P ,~5-20% and V S ,~10-30%) can be explained by the existence of wüstite. The FeO velocity in this study at CMB conditions is larger than that found in the study of Wicks et al. (2017). This implies that a much higher amount of FeO is needed to fit the ULVZ velocity. The addition of wüstite would cause not only a velocity decrease but also a drastic density increase. It is difficult to explain all ULVZs by FeO enrichment. An extremely large increase in density (20-25%) accompanying the ULVZ has been reported below the Philippine islands (Idehara 2011). Some of the increase in the ULVZ density could be explained by the existence of wüstite at the base of the lower mantle.

Conclusions
We measured the longitudinal sound velocity and density of wüstite up to 112.3 GPa and 1700 K using IXS and XRD. Because the sound velocity of wüstite is the slowest of the major mantle minerals in the lower mantle, a wüstite enrichment could cause a low-velocity anomaly, such as that observed in ULVZs. Therefore, wüstite likely plays an important role in generating the heterogeneities observed seismologically in the deep lower mantle.
Abbreviations ULVZ: Ultra low-velocity zone; CMB: Core-mantle boundary; LHDAC: Laserheated diamond-anvil cell; BIF: Banded-iron formation; DAC: Diamond-anvil cell; IXS: Inelastic X-ray scattering; FWHM: Full width at half maximum; XRD: X-ray diffraction; LA: Longitudinal acoustic peak; TA: Transverse acoustic peak; PREM: Preliminary reference Earth model Fig. 6 Sound velocities of wüstite under lower mantle conditions. The V P (a) and V S (b) profiles were calculated along the mantle geotherm (Brown and Shankland 1981). The red solid line represents the B1-FeO values obtained in this study. The dashed and dotted lines represent bridgmanite (X Mg = 0.94) and magnesiowüstite (X Mg = 0.79), respectively (Murakami et al. 2007). The bold line represents PREM Fig. 7 Comparison of the sound velocities of wüstite with those of PREM and ULVZs. The V P and V S profiles of wüstite are shown by broken lines as a function of pressure along the mantle geotherm (Brown and Shankland 1981). The V P and V S profiles for PREM are plotted by solid lines with those of the ULVZs